# HSC Extension 1 and 2 Mathematics/3-Unit/HSC/Primitive of sin and cos squared

From Wikibooks, open books for an open world

The integration of these functions can be performed by the substitution of or by a function in terms of respectively.

## Deriving the substituted functions[edit]

By the double-angle formula, . Rearranging to make the subject, .

We know by the Pythagorean identity that , so . Rearranging, .

## Finding the primitive[edit]

By substituting for , . Similarly for ,

These can be integrated by using the primitives of cosine and sine

For *cos ^{2} α*

For *sin ^{2} α*